Is the equation (8–√4)−24⋅(8–√)16=8−48

Question

true or false? Select the response that correctly answers the question and provides the appropriate justification.(1 point)
Responses

True. When the bases are multiplied, the exponents are also multiplied.
True. When the bases are multiplied, the exponents are also multiplied.

True, but the equation can be simplified further.
True, but the equation can be simplified further.

False, because the exponents should be added rather than multiplied.
False, because the exponents should be added rather than multiplied.

False, because the Negative Exponent Rule should be applied.

Answer 1

To evaluate the equation \( (8 - \sqrt{4}) - 24 \cdot (8 - \sqrt{16}) = 8 - 48 \), let's simplify both sides step by step.

First, simplify \( \sqrt{4} \) and \( \sqrt{16} \):

• \( \sqrt{4} = 2 \)
• \( \sqrt{16} = 4 \)

Now, substitute these values into the equation:

• Left Side: \[ (8 - 2) - 24 \cdot (8 - 4) \] Simplifying further: \[ 6 - 24 \cdot 4 = 6 - 96 = -90 \]

• Right Side: \[ 8 - 48 = -40 \]

Now, we compare both sides:

• Left Side: \(-90\)
• Right Side: \(-40\)

Since \(-90 \neq -40\), the equation is false.

Therefore, the correct response would be: False, because the exponents should be added rather than multiplied. (Note: This statement is somewhat misleading; the main issue here is that both sides do not equal, not necessarily about exponents in this specific case, so the reasoning is slightly off, but it denotes falsehood.)